a hit I don't understand

[wouter meeussen]

1,2,4,5,8,10,16,20,32,40,64,80,128,160

"A094958 = Numbers of the form 2^n or 5*2^n.
Comments:  The subset {a(1),...,a(2k)} together with a(2k+2) is the set of proper divisors of 5*2^k.
For a(n)>4: number of vertices of complete graphs that can be properly edge-coloured in such a way
that the edges can be partitioned into edge disjoint multicolored isomorphic spanning trees."

Integers k^2 having no Sum-Of-Squares-Representations of k^2 = a^2+b^2+c^2 with c>=b>=a>0 .
In plain, k^2 cannot be a sum of three non-zero squares.

Why would "Numbers of the form 2^n or 5*2^n" have that property?

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Mma code:

<< NumberTheory`NumberTheoryFunctions`

Table[Length at Cases[SumOfSquaresRepresentations[3, k^2],
    q_List /; FreeQ[q, 0], {1}], {k, 96}]

Position[%, 0] // Flatten
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W.